| Topic for open discussion:
Topological Surgery Theory
for AWES Design and Operations |
|
Send
AWE notes and topic replies to editor@upperwindpower.com
|
| ?next? |
| October 4, 2020, post by Dave Santos Topological Order itself as Macroscopic QM Basis Macroscopic quantum phenomena The editors of the article let be: (emphasis added) "The best-known examples of
macroscopic quantum phenomena are superfluidity and superconductivity;
other examples include the quantum Hall effect, giant magnetoresistance
and topological order."
|
| Aug. 10, 2020, post by Dave Santos Kite Lattice Topologies and Surgery Theory Just to make it a bit clearer to Yuri where we are at theoretical kite lattices- Topological Chemistry is close advanced "kitematter" similarity case, even as we barely start to see the basic two-line steerable power or arch kite as a toroid/coffee-cup/donut object. Our domain starts as a toy-problem like chess, but the combinatorics are still effectively intractable. It gets really hairy when we try to integrate wind-field structures with our polymer lattices, whose wakes are real vortex-lattices. There is pure new science, and trivial and practical engineering aspects. Its all a starting pastiche, a primordial soup. What we do know is that the simple geometric view and primitive equations of motion are not enough to validate contending kite architectures. Kites are a terrific quantum analog model, superposed wave functions everywhere. Planck's Constant defined non-dimensionally, such that the quantum-of-action matches our scale, recovers QM. KiteMatter is the killer-app of quantum metamaterials. Topological Quantum Groups is clearly a bridge between what kite dynamics are telling us about their topological identifications. Our engineering expertise with lines, membranes, knots, lattices, and so forth, is a nice back-flow of mathematical inspiration. |
|
Aug. 9, 2020, post by Dave Santos
Kite Lattice Topologies and Surgery Theory Hi again Yuri, There
is increasing academic interest in applied topology for classifying and
maybe optimizing theoretic kite energy lattices. Of course, the
mathematical physics of aerospace has so far hardly intersected with
your field. Our initial interdisciplinary cross-mapping has identified
Surgery Theory as the right stuff for formalizing dynamic
reconfigurations of our networks to match load and wind conditions. We see our standard industrial mechanical connectors as surgical operators. Traditional
kites inherently rely on braids and knots. If nothing else, its all a
great educational analog to the basic mathematics.
Funny
thing is that there hardly seems to be prior cross-analysis of complex
mechanical networks with abstract topology. Of course there is
fundamental advanced physics application of topology, much of it
speculative. There are intriguing beginnings of fluidic topology, like
vortex lattices. What we are not seeing is who is working on
higher-dimensional multi-modal real-world topologies, that might take
an interest in our domain. Who knows, you may become the go-to topology guy in Airborne Wind Energy Lattices R&D.
Hope your thesis work has gone well. Thanks again for those study references. Let
us know of any related research direction that comes to mind. We have
enough going for you to look over and make suggestions. Maybe see you
around, as before...
Cheers,
dave
kPower
|
| Aug. 9, 2020, by Dave Santos Topological Surgery Theory for AWES Design and Operations A huge AWES engineering design issue is whether an AWES should be topologically constant or variable. Kite Sports, as an AWE class, all depend on variable topologies to optimally match conditions; a constant changing of kites, lines, and bars from a "quiver". Topology is a relatively new revolutionary major branch of mathematics, and Surgery Theory even newer, as a "a major tool in high-dimensional topology". However, topological surgery is ancient and still ubiquitous in industrial practice; whenever a crane makes a lift, a train is configured, a ship docks, or any standard connector is coupled or uncoupled. Therefore, its reasonable that AWES will include topological surgeries in their basic principles-of-operation. Such surgeries include moving anchor-points around a circle as prevailing wind veers, and hot-swapping multi-tethers and array unit-kites. Unit-kites may even swarm from airports to dynamically configure over widely located kitefarms. Surgery is a scaling method. Any field engineer knows that topological surgery operations are not just feasible, but essential. Its time for academic theorists to embrace topological surgery in their scope of AWES research. |